Lotka's seminal work ( Lotka A. J. , Proc. Natl. Acad. Sci. U.S.A. , 6 (1920) 410) “on certain rhythmic relations” is already one hundred years old, but the research activity about pattern formations due to cyclical dominance is more vibrant than ever. It is because non-transitive interactions have a paramount role on maintaining biodiversity and adequate human intervention into ecological systems requires a deeper understanding of the related dynamical processes. In this Perspective we overview different aspects of biodiversity, with focus on how it can be maintained based on mathematical modeling of the last years. We also briefly discuss the potential links to evolutionary game models of social systems, and finally, give an overview about potential prospects for future research.

中文翻译：

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循环相互作用驱动的模式形成：近期发展简述

洛特卡（Lotka）的开创性著作（洛特卡AJ（Lotka AJ），美国国家科学院学报（Proc。Natl。Acad。Sci。USA），6（1920）410）已经有100年的历史了，但是关于由周期性优势引起的模式形成的研究活动更加活跃。比以往任何时候都好。这是因为非传递性相互作用对于维持生物多样性具有至关重要的作用，而人类对生态系统的充分干预要求对相关的动力学过程有更深入的了解。在本《观点》中，我们概述了生物多样性的各个方面，重点是如何根据最近几年的数学模型对其进行维护。我们还简要讨论了与社会系统进化博弈模型的潜在联系，最后，概述了未来研究的潜在前景。